Definition of Phenomena as "Limit" and "No-Limit"

The first axiom of the argument is a simple one: what we understand of all phenomena, at minimum, is strictly an observation of space. It is the one universal axiom which exists as the limits that give structural boundaries to reality. In a separate and simultaneous respect, it is absent of the very same definition as no-limit. Space observes a dualistic nature of limit and no-limit.

Observing the definition of space, within any given dictionary source, one is placed into a paradox. A whole host of definitions are given, which include but are not limited to: “area” “volume”, “dimension”, and “limit” (Space, 2018) (Space, 2018) These definitions, summated under the last definition as “limit”, reflect back upon the process of definition as a form of limit in itself by which a phenomena exists through the inherent limits which form it. Space as limit is limit through space, with the observation of any dictionary definition resulting in a dualistic circular and linear form of reasoning where one definition leads to another while simultaneously circling back to the original. Under these terms circular rational is justified through inherent linear elements and vice versa while observing, under certain degrees, Mirimanoff’s concept of “wellfoundedness” in which the definition as a set of information contains no infinite descension (Levy, (2002)(1986),(1988)) further implying an original source.

This dualism of progressive linear and circular definition provides a limit in itself through a process of mirroring in which the further corresponding definitions in turn follow this same process.The axiom of space follows this definition process in which a limit reflects itself through a further limit, rationally in both form and function as circular, and reflects further limits, rationally in both form and function as linear, in which an observation of no-limit occurs. This observation of “no-limit” is founded inherent within the dictionary definitions of space in an immediate respect within the aforementioned definition itself (Space, 2018). In a separate respect, function follows form where these definitions reflect through further definition ad-infinitum in a dual circular and linear regressive/progressive manner. Limit and No-Limit are dependent on a dual form of circular and linear reasoning that simultaneously manifests further definition while maintaining there own under spatial terms.

This dualistic understanding of space can further be observed in many of the works of the pre-socratic including but not limited to the Pythagoreans and Anaximander. The Pythagorean Philolaus observed “that all things in the universe result from a combination of the unlimited and the limiting; for if all things had been unlimited, nothing could have been the object of cognizance.” (Smith, 1870) Aristotle observed “[the Pythagoreans] plainly say that when the one had been constructed, whether out of planes or of surface or of seed or of elements which they cannot express, immediately the nearest part of the unlimited began to be drawn in and limited by the limit.” (Smith, 1870) He further implied that the Pythagorean teaching of the limit and no-limit were direct results of the philosopher Anaximander who argued “(that which is) unlimited”, “boundless”, “infinite”, or “indefinite” as “Apeiron” (Liddell & Scott) and “peras” as “end, limit, boundary”. (Liddell & Scott)

Modern philosophical instinct and training implies the definition of space as limit and no-limit in dual linear and circular terms questionable considering one is presented with two perspectives: They are an empirical contradiction (Horn, 1989) (Smiley, (1993)) or a transcendental paradox (Smith W. K., 2011) (Zhang, 2015) (Bowen, 2016) in the respect that logic either nullifies itself or transcends pasts its origins. (quote) Neither school of thought gives any real justification as they manifest a dualism in which one perspective attempts to wrestle over the other, resulting in a Neitschian view of force embodied as “perspectivism” (Neitzche), Pythagorean definition where duality is conduce to change (Kahn), or the problem of Wittgenstein where “[a]ll the propositions of logic are generalizations of tautologies and all generalizations of tautologies are generalizations of logic. There are no other logical propositions.” (McGuinness, 2008)

Paradoxically, the western empirical linearism and eastern transcendental circular forms of logic, both need eachother as one exists as the “limit” which defines the other. The western laws of logic observe the “fallacy of circularity” (Dowden, 27 March 2003) as a justification for linearism. The eastern views observe the deficiencies of individuative linearism promote holistic circularity. (Biao, (JULY - AUGUST 2002)) (I Ching) In a separate respect both observe a nature of “no-limit” through western regressive and progressive rationality dependent to a degree on infinitism (Klein & Turri) (Klein, "Human Knowledge and the Infinite Regress of Reasons", 1999) and eastern circularity dependent on holisitic centering and rotation as absent of limit. (Biao, (JULY - AUGUST 2002)) (Ma, June 5, 2009)

The problem occurs in the respect that we are constantly limited to dualisms, and the problems of logic and definition are reduced to ones of dimension. These dualisms create a problem of definition dependent upon polarity, observed in the hermetic philosophy as the “Principle of Polarity” (Atikinson, 1912). One polarity defines the other while simultaneously causing a perpetual sense of definition between the two. Polarity can be viewed as a contradiction of force under the Nietzschean metaphors of Apollo and Dionysus (Neitzche F. , 1872), an absence of structure as the Pythagorean Dyad (Kahn), and an alternation of definition through the hermetic “Principle of Frequency” (Atikinson, 1912). Or it may simply just be observed as a problem in the same manner of Cartesian Dualism (Robinson) and Platonic Dualism (Robinson) leading to the competing substance, property, and predicate dualistic perspectives (Robinson) that provides for the universal means of division in philosophy between materialism and idealism (Priest, 1991) (Novack, 1979).

A third more rational approach must be taken in order to deal with the multiple dualisms inherent through the limit and no-limit definitive nature of space in both form and function, quantity and quality, circularity and linearism, and western empirical and eastern transcendental logic. Without a solution to these reoccurring duals a process of fracturing takes place in which each definition is dependent on an infinite linear regression, circular justification or simply an acceptance of the axioms without any observable definition, all of which are observed in the Munchausen Trilemma (Albert, 1968). This fracturing can be implied as a form of logistic Atomism, observed by the more modern philosophers Russel, Wittgenstein and Carnap (Carnap, (1934)) and stemming from the pre-Socratic philosophers Leucippus and Democritus of Abdera (Seyffert, (1894)), in which the linear regressive separation, circular definition, and axioms can be observed as individual units in themselves that must relate through a process of continual change. Hence it may be implied that dualisms are dependent on relativistic logistic unit-particles that exist through continual individuation as a form of definition.

The problem occurs in the respect that the very problem of definition we seek to avoid, change, appears to be one of the very foundations for this very act of definition. We can simply observe this as relativity merely being individuative limits and no-limits that exist as spatial dimensions of change as unit-particulate. This provides the foundation for not only materialistic change as a refutation of idealism observed by Kant (Kant, Archived 6 February 2007) (Kant, Critique of Pure Reason (NKS translation)) , further evidenced by physics dependence on Principle of Locality in the Principle of Relativity (Salençon & Lyle, 2001), but further change in abstract logistic structures such as moral relativism (Swoyer, 2003), truth and cultural relativism (Baghramian), methodological relativism (Collins, 1998), relationalism (Baghramian M. , 2004) and dialectic materialism (Thomas, 2008). However, the observation of change as a constant, through logisitic unit-particulate, observes a consistency. This can be summated into a paradox or contradiction, however considering these dimensions exist in themselves as foundations of the argument from which both side gains definition, this further results in another dualism. In this instance it is an observation of change and no-change. The problem is further exacerbated by the number of aforementioned dualities premised in spatial limit and no-limit.

The solution to the dualism lies within the axiom of the problem: our understanding of phenomena is often times one of quantitative and qualitative spatial dimension, in this case a dualism. In turn this Dualism results in a third dimension, as one dimension in itself, which maintains the dualism while simultaneously justifying it and providing logical grounds through a medial center point conducive to origin.

Re: Definition of Phenomena as "Limit" and "No-Limit"

If every observation is of space as what limits and provides structural boundaries, why consider a space itself as not limited? A space independent our conception of space. Also, does change relate to a space itself? As how could space remain unlimited and yet our observations of space are always changing? What is unlimited cannot be changed, or it would have constraints and would be limited. An observation of the unlimited would be endless,and not subject to change or time as constraint. Otherwise, how would an observation end. Hume said, perceptions are simple and indivisible,ruling out any infinite observations, and if there were such things, they would run concurrently.

Re: Definition of Phenomena as "Limit" and "No-Limit"

Also, if boundaries were without boundaries, would they still be boundaries? I tried to imagine a wall without an end, but a wall without an end cannot be imagined because my thoughts were full of wall. I couldn't imagine going over the top of the wall, immeasurably tall, couldn't get to the end, immeasurably long, and then the wall began pushing me backwards, immeasurably wide. The wall was no longer a boundary, because it could no longer act as a limit, due to an inability to be observed. How can what is not observed be a boundary? Boundaries, like rules, presuppose observance.

Last edited by Inrealtime87 on June 26th, 2018, 5:07 pm, edited 1 time in total.

Re: Definition of Phenomena as "Limit" and "No-Limit"

Inrealtime87 » June 26th, 2018, 4:41 pm wrote:Also, if boundaries were without boundaries, would they still be boundaries? I tried to imagine a wall without an end, but a wall without an end cannot be imagined because my thoughts were full of wall. I couldn't imagine going over the top of the wall, immeasurably tall, couldn't get to the end, immeasurably long, and then the wall began pushing me backwards, immeasurably wide. The wall was no longer a boundary, because it could no longer act as a limit, due to an inability to be observed. How can what is not observed be a boundary? Boundaries, like rules, presuppose observance.

A boundary without boundary observes the boundary existing ad-infinitum in the respect it never changes. Take for example a folding line. You can fold it a million different ways but at the end of the day all those "folds" are still fractions of the original line itself...the line is always present through itself and acts as its own measurement system.

The problem of infinity is that it is an absence of limit, hence it is negative in nature. It can be observed if and only if there is a limit. So we cannot observe a point without some limit extending from it.

Now if I look at a "point", it is quite literally an observation of infinity as it is without end. The problem occurs in the respect the point is 0 dimensional. So while the line may project ad-infinitum with the 0d point as proof, the 0d point is in itself not infinite...it is not anything.

Now if we take the same nature of point and observe it as 1 dimensional it means it must be directed somewhere. The problem occurs in the respect it must be directed towards itself otherwise it takes some other form than a point and in effect becomes a line (straight or curved) and the preceding volume of space which comes with such things.

So the point must always be absent of structure...however if it is an entity in itself it must also have structure. So a problem occurs: The 1d point must have structure and no structure simultaneously...it must be limit and no limit.

The point as "direction" through infinite movement in turn observes "direction", through the 1d point, as the foundation of all limits. The point directed into itself ad-finitum enables it fundamentally to exists as 1 direction through infinity directions, as 1 infinity. So the point, directed into itself through infinite directions, observes an absence of finiteness in one respect while simultaneously observed this infinite movement as one direction in itself.

****I may have to elaborate more if I don't appear clear to you.

To build off of my point all limits exist as boundaries of movement which are composed of movement in themselves, considering all limits are composed of further limits. For example if you break line down it is fundamentally composed of further lines...all parts are composed of further parts with "divergence" being the means of movement as separation.

The problem occurs in the respect that this divergence in itself acts as a spatial boundary. If you separate a line into two lines, the space between them is still a boundary of potential movement considering the lines may only reconnect at the tips (in this example) with these tips of the lines always existing in a linear manner between the two.

Potentiality, acts as negative boundary in these respects with the lines existing as localized actual boundaries. However potentiality and actuality only exist if they alternate through eachother. A localized reality results in a potential with the potential in turn becoming localized and a process of alternation continues. This alternation as a constant movement in itself is an approximation of an infinite revolution which may exist at one moment.

The limit exists fundamentally as movement, with any lack of movement fundamentally being an absence of being. However this negative limit is strictly relativistic considering from a seperate angle of time it is a localized reality. Hence the nature of limit and no limit are dependent upon the angle of observation as both alternate through eachother.

However if they both alternate through eachother, at one infinite moment, we are left with a 1 dimensional point of pure movement with no finiteness to it. Direction through movement, as the foundation of limit, in turn provides the foundation of all boundaries as a limit in itself while simultaneously being infinite.

In simpler terms we view infinity through observing the point as the point in itself is constant.

If this is not clear, ask further questions.

To simplify it:

Limit and no-limit exists through eachother as movement through direction with movement through direction in itself being both limit and no-limit. The definition is an expanding circle so to speak where the premises are maintained through the definitions depending on eachother while a progressive expansion allows for linear progress.

The point as infinite can simultaneously act as a field so if approaching a point ad-infinitum, any perceived "emptyness' (or fullness in regards to the 1d point) is merely an observation of the point itself.

Blanking your mind to pure white would be a hypothetical example of perceiving the 1d point as a field.

Re: Definition of Phenomena as "Limit" and "No-Limit"

Would you say we observe 1d in instances other than mind blanking?Though there is the causal inference of 1d from there being other dimensions.

Is the perception of a color an observation of 1d? It's not apparent to me that it is. Is a color the same as a point in space, as a boundary? Though admittedly all boundaries must be colored to be observed. Would you say color is a boundary, or only a quality of a boundary? Can a color be two or three dimensional like a boundary? Does color have structure? For color to have structure, there would have to be color in itself wouldn't there? If blue could be large or small wouldn't it have to take some shape? Then it would be a large blue square or some other shape.But then how is there color in itself if it takes a shape?

Also, do we observe points or is their existence inferred through causality? The idea the what we see must be made up of something.

Also, would you say causal inferences are necessary ones, seeing as how they are an assumption of a reoccurring past perception? Considerations of things in themselves are causal inferences, but how is the foundation of causal inferences, past perceptions, able to describe what cannot be perceived? The 1d. This is a question i've always had. How is it we are able to talk about what is seemingly impossible to perceive? Like 1d points or objectivity or nothing, and we do this with some comprehension. These things must lie in perception somewhere.

Is the perception of a color an observation of 1d? It's not apparent to me that it is. Is a color the same as a point in space, as a boundary? Though admittedly all boundaries must be colored to be observed. Would you say color is a boundary, or only a quality of a boundary? Can a color be two or three dimensional like a boundary? Does color have structure? For color to have structure, there would have to be color in itself wouldn't there? If blue could be large or small wouldn't it have to take some shape? Then it would be a large blue square or some other shape.But then how is there color in itself if it takes a shape?

Also, do we observe points or is their existence inferred through causality? The idea the what we see must be made up of something.

Also, would you say causal inferences are necessary ones, seeing as how they are an assumption of a reoccurring past perception? Considerations of things in themselves are causal inferences, but how is the foundation of causal inferences, past perceptions, able to describe what cannot be perceived? The 1d. This is a question i've always had. How is it we are able to talk about what is seemingly impossible to perceive? Like 1d points or objectivity or nothing, and we do this with some comprehension. These things must lie in perception somewhere.

Would you say we observe 1d in instances other than mind blanking?Though there is the causal inference of 1d from there being other dimensions.

Yes and No at the same time in different respects. We can observe 1d space relative to other 1d spaces, where each 1d space acts as a part so to speak. In these respects we can observe 1d as a unit in the respect it folds through other 1d spaces (think of line composed of 2 lines running parallel).

In a seperate respect where we observe 1 dimension as Unity (rather than unit, which is an approximation of unity), we cannot observe everything at once.

Is the perception of a color an observation of 1d?

Considering color is actually composed of frequencies, with a frequency being (argued as) a 1d line folding through itself, what we understand of as color is premised in a linear limit. The color, as an approximation of these frequency still observes certain limits in the respect red is not blue, but exists as a limit in itself. Red may progress to blue, through a series of infinite fractal colors, however this would be equivalent to a numerical example of 3 tending toward 4 through an infinite number line:

Each color, as a limit in itself, progresses linearly to any color it is moving towards, with this progression defined the relations of the colors as a limit in itself.

It's not apparent to me that it is. Is a color the same as a point in space, as a boundary? Though admittedly all boundaries must be colored to be observed. Would you say color is a boundary, or only a quality of a boundary?

See above. What we understand of quality, if all phenomena are composed of frequencies, is merely an approximation of quantity (ie see color) where the quantity in one respect becomes "indefinite" yet still exists as both 1 and many in a separate respect. So a quality is still quantifiable in itself as "1" through which many, or possibly infinite, grades exist as a a series of relations which compose it.

A quantity is a quality in itself, in the respect it is a direction so to speak. If I quantify an empirical object, as 1 or 2 or 3, what I am observing is a series of directions in respect to the object moving through time. So if I quantify an orange as "1", what I am observing is "1" as fundamentally acting as direction through time...in these respect 1 as a finite unit is an observation of temporarility where any percieve quantity exists if and only if it is directed.

In these respects all quantity maintains a qualitative aspect of direction as movement through the limit of the line.

Can a color be two or three dimensional like a boundary?

Color as movement, through its inherent nature of being a frequency, would require a minimum of two dimensions in the respect that it must progress from an actual location to another actual location through potentiality. All movement requires an inherent dualism of actuality and potentiality when the movement itself is finite, such as in the case of color. So at minimum, color as a finite reality, is 2 dimensional and consists of the inherent movements which form empirical reality.

Color as three dimensional, in theory, would possibly be three dimensional in the respect that the linear progression of color as being vertical exists relative to horizontal movement and depth. This triad of movement exists relative to other lines and what we understand of vertical/horizontal/depth is linear movement which cycles through itself where what is vertical alternates to horizontal or depth.

For example if I move in a vertical direction it exists as a horizontal movement relative to the beginning point of measurement. This beginning point of measurement exists if and only if there is a framework in which the vertical line exists. In simpler terms, the vertical line cannot project vertically (even if it is singled out) unless there is some other direction it exists in relation to, hence if I alternate the beginning point of measurement so that the vertical line becomes horizontal it would require a seperate linear construct to eventually rotated along with it to dually takes its place as direction exists through other direction that is fundamentally an inversion of the prior....

So a color, as a directed frequency, would exist relative to another color of a seperate direction and alternate to being vertical, horizontal and movement as depth relative to other colors which are directed in different means.

So a color may have a vertical direction, but relative to another color it is horizontal, while relative to another it is moving through depth....if any of this makes sense.

Does color have structure? For color to have structure, there would have to be color in itself wouldn't there?Color quite literally, as a frequency, is the relation of linear boundaries with these frequencies existing through time as fundamentally directed movement. As finite linear relations, it in turn exists as another linear movement through time itself.

Color in itself is dependent upon its demarcation where red may be seperate from blue, or unified through purple, but this act of qualification is fundamentally an act of localization in which each color, from a perspective of time exists as a temporal locality in one respect.

For example if I view Red as a localization of time, in which all other finite movements exist both through and relative to it I would observe an infinite number of objects extend through it (such as brick, cherry, or dress, etc.) hence Red exists as a means of movement for a variety of localities.

If blue could be large or small wouldn't it have to take some shape? Size is an observation of movement and relation. For example I may view a cat expand, then shrink, through time (alternation of expansion and contraction) while its size is relative to other cats so to speak in which the cat may be "smaller" than another cat at "x" distance however at "y" distance it becomes relativistically larger. The cat may always be "larger" than the other cat when viewed in relation to certain constant objects which mediate the space between them (such as the blades of grass in a field maintain a constant set of size ranges)...so size maintains a trifold nature of movement as moving towards, moving away, and the general framework through which they move (with this framework always maintaining the size of the cats as relativistically constant.

Now this movement, as the relativistic approximation of one locality to another, would in theory necessitate color to have size in certain respects in the respect it exists through localization. For example while we maintain the brick (as a set of linear dimensions, hence frequencies) as "red" (as a set of linear dimensions, hence frequencies), we may invert the beginning point of measurement from "brick → red" to "red → brick" where the relation of one beginning locality effectively results in the formation of another. With red, existing through the "brick" (and a variety of other localities) as a size in itself it effectively becomes larger or smaller through the other localities in which it not just exists but exists as movement (such as the red paint on a part being of greater size/volume [but less density] than the brick itself).

Then it would be a large blue square or some other shape.But then how is there color in itself if it takes a shape?

Color exists in itself, through shape, as being founded in linear dimensions just in the same manner as a shape

Also, do we observe points or is their existence inferred through causality? The idea the what we see must be made up of something.

If we look at the nature of causality it is an observation of structure. A exists as a cause for B with B being an extension of A in one respect, as a cause, while being an approximation of it (or limit of unity) in the respect it exists as effect. Causality, while observed through time, is fundamentally an observation of structure that is ever present, hence is an observation of an approximate unity and while existing through time is not limited to time in itself. As everpresent through structure, cause is fundamentally timeless as structure, hence infinite in the respect it is an extension of one.

The point as 0d would observe causality as movement through direction by the 1d line, where the 1d line provides a foundation of "form as movement" that provides the necessary boundary for structure itself. If we take a theoretical perspective of a 1 dimensional point, where the forms exist as approximation of a 1d point through -1 dimensional lines which lack direction in and of themselves but exist through the 1d point (as intradimensional) we observe causality as a constant form through the point.

I may have to elaborate further on the above.

We view causality through 0d points and 1d lines as movement, with this movement being an inversion of the 1d point and -1d line as an approximation of it. In simpler terms, infinite movement of one (similiar to parmenides perspective) exists as no-movement, however it is approximated as movement through multiplicity.

In these respects color maintains a dual nature of being an extension of the 1 as 1 in itself, hence is constant and never changing, while in a seperate respect is observed approximately through relativistic change through 0d space as acausal. Color is uncaused cause where acausality (through the 0d point) is observed as multiplicity and causality (through the 1d point) is unity through unity.

Also, would you say causal inferences are necessary ones, seeing as how they are an assumption of a reoccurring past perception?

See above, causality is an observation of constant timeless structure as an extension of a 1 dimensional infinite structure.

The past perception, as a continual structure which exists through the present and the future observes that while time is percieved as being trinitarian it exists as one eternal movement from a seperate unified point of measurement. Time is a structure, one which can theoretically be construct much like one constructs a house, that exists an an approximation of unity.

While a past perception is subject to gradation, as perception itself is a structure in its own respect as it exists through the application and maintainence of inherent limits, it exists as both causal and acausal in these respects:

All observation exists through limits, where we both maintain and manifest these limits through the limits themselves (a line manifests through a line, as a line is always a line regardless of its place with its place being fundamentally a ratio of itself). All observation exists simutaneously as acausal in the respect it exists through 0 dimensional, under the 0d point which exists as a point of change or approximation through inversion.

In a separate respect it is composed of the very same limits it manifests. For example, consciousness may observe the line, but is it the line which forms consciousness?

Considerations of things in themselves are causal inferences, but how is the foundation of causal inferences, past perceptions, able to describe what cannot be perceived? The 1d. This is a question i've always had. How is it we are able to talk about what is seemingly impossible to perceive?

Because talking itself is a limit, one which exists linearly through time much like a frequency. Take for example the previous underlined sentence. It is dependent upon the replication of certain conceptual boundaries (such as the letter "a" repeats itself in a manner where if viewed as a beginning point of measurement it repeats itself, through multiplicity as there are multiple "a", with these multiple "a"'s causing the sentence to curve around it. "a" as a locality which becomes non-localized through the sentence itself where its placement eventually causes the same "a" to curve the "localities" of the surrounding area (such as "c" or "u" or "e"). "a" as a locality which curves the other localities.

The reason I say this is that we see limit for what it is the universal axiom which is the foundation of axioms as its own limit.

Take for example the question: "What is space?" The answer: Space is "what" with "what" being an extension of objective/objectivity where this in itself is "limit" with limits existing through space as being composed of space with space through space being "limit" itself. The circular/linear reason (which is simultaneously, provides the very same limit of definition for the question itself.

The limit is the foundation of empirical and abstract realities, as fundamentally being both and considering these realities are limits in themselves.

Like 1d points or objectivity or nothing, and we do this with some comprehension. These things must lie in perception somewhere.